For the G-ROM (REF ), the numerical analysis started two decades ago with the pioneering work of Kunisch and Volkwein, who proved the first error bounds for the POD of parabolic equations, e.g., the heat equation [1]} and the Navier-Stokes equations [2]}.
More than a decade later, Singler improved Kunisch and Volkwein's results, by proving sharper error bounds [3]}.
Recently, optimal pointwise in time error bounds were proved in [4]}.
These results finally bring the G-ROM numerical analysis to a level comparable to (although not as developed as) the level of the numerical analysis of the FEM.
